In this post-apocalyptic future, the "known world" seems restricted to North America.
See also Are there other governments in The Hunger Games world?, a question on another SE site. Throughout the Hunger Games series, there is never any mention of societies or even geographic locations outside of North America. It seems that whatever disaster brought North American society to this post-apocalyptic state also either destroyed the rest of the world too or at least severed it from Panem's part.
It's still possible that there are other human societies out there, maybe in a worse state technologically than the Capitol and Panem. But the new rulers of North America either don't have the resources, or don't have the capability, to go out and re-discover those parts of the world. It seems they're content with ruling their own continent and don't even bother about the rest of the world. It's no threat to them, so they're content to live and let live.
So yes, the Capitol does control the known world, but its influence doesn't extend beyond North America. It probably does, though, extend beyond what's now the United States: see Where were the locations of the districts in The Hunger Games? Although there's no clear information on exactly where the districts and locations of Panem are relative to today's geography, it's at least a strong possibility that parts of what's now Canada and Mexico are also included. There'd be no particular reason for a future post-apocalyptic state to respect our time's borders, anyway.
